Information on Result #1856279
There is no (6, m, 51)-net in base 7 for arbitrarily large m, because m-reduction would yield (6, 99, 51)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(799, 51, S7, 2, 93), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 875812 076998 063930 757182 152801 734486 857625 591237 003207 471162 651133 531677 095424 480008 / 47 > 799 [i]
Mode: Bound.
Optimality
Show details for fixed m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No (6, 50)-sequence in base 7 | [i] | Net from Sequence | |
| 2 | No (6, 6+k, 51)-net in base 7 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (6, m, 51)-net in base 7 with unbounded m | [i] | ||
| 4 | No digital (6, 6+k, 51)-net over F7 for arbitrarily large k | [i] | ||
| 5 | No digital (6, m, 51)-net over F7 with unbounded m | [i] | ||